{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6237OTQVNPR2BAUAL7QEUWZZWP","short_pith_number":"pith:6237OTQV","canonical_record":{"source":{"id":"1512.04360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-14T15:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"a85658ce5584dec41b368b20b85e82eef21d0a3c5b1f928bedf9f48c4b0bc526","abstract_canon_sha256":"ee5bebc4c377f40befc9491c4f0e17b7d72728b1272743cb44a598c2a7103b2b"},"schema_version":"1.0"},"canonical_sha256":"f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2","source":{"kind":"arxiv","id":"1512.04360","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04360","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04360v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04360","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"6237OTQVNPR2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6237OTQVNPR2BAUA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6237OTQV","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6237OTQVNPR2BAUAL7QEUWZZWP","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04360","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-14T15:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"a85658ce5584dec41b368b20b85e82eef21d0a3c5b1f928bedf9f48c4b0bc526","abstract_canon_sha256":"ee5bebc4c377f40befc9491c4f0e17b7d72728b1272743cb44a598c2a7103b2b"},"schema_version":"1.0"},"canonical_sha256":"f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:22.383476Z","signature_b64":"NBR5EoHvhPf+nabJn5h7LbwypLUZkI59B9ixrSBqPIeNDUzj27nHjB28LKchjsei64xFuerOdz2Vjx/cRAVJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2","last_reissued_at":"2026-05-18T01:24:22.382865Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:22.382865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04360","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLgfxjxiDCHH8vht9wEl+bidOnKnGu9f1EEjHdhXplGjyHM2zENB6l+mSP+FD2WVa5l6uq9cazjg0VjVdviJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:06:06.393099Z"},"content_sha256":"35e9a527d199d8ac1eab60f8c31521c152647202a1bd55f536f399824c5f9832","schema_version":"1.0","event_id":"sha256:35e9a527d199d8ac1eab60f8c31521c152647202a1bd55f536f399824c5f9832"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6237OTQVNPR2BAUAL7QEUWZZWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variations on a Theorem of Birman and Series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Anna Lenzhen, Juan Souto","submitted_at":"2015-12-14T15:21:33Z","abstract_excerpt":"Suppose that $\\Sigma$ is a hyperbolic surface and $f:\\mathbb R_+\\to\\mathbb R_+$ a monotonic function. We study the closure in the projective tangent bundle $PT\\Sigma$ of the set of all geodesics $\\gamma$ satisfying $I(\\gamma,\\gamma)\\leq f(\\ell_\\Sigma(\\gamma))$. For instance we prove that if $f$ is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04360","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKAwwoMqkGm/yyOb/535zH1vvJ7HZkEOXueYxzAxT4Jf+5xK0xaWrZeJFDR1uNGECPol1QlbK3xaBb3sFSxdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T16:06:06.393500Z"},"content_sha256":"2cd1940eeb859d7989559047dfdb73a0f8274db4beaeed9d2367671045dd0be2","schema_version":"1.0","event_id":"sha256:2cd1940eeb859d7989559047dfdb73a0f8274db4beaeed9d2367671045dd0be2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6237OTQVNPR2BAUAL7QEUWZZWP/bundle.json","state_url":"https://pith.science/pith/6237OTQVNPR2BAUAL7QEUWZZWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6237OTQVNPR2BAUAL7QEUWZZWP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T16:06:06Z","links":{"resolver":"https://pith.science/pith/6237OTQVNPR2BAUAL7QEUWZZWP","bundle":"https://pith.science/pith/6237OTQVNPR2BAUAL7QEUWZZWP/bundle.json","state":"https://pith.science/pith/6237OTQVNPR2BAUAL7QEUWZZWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6237OTQVNPR2BAUAL7QEUWZZWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6237OTQVNPR2BAUAL7QEUWZZWP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ee5bebc4c377f40befc9491c4f0e17b7d72728b1272743cb44a598c2a7103b2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-14T15:21:33Z","title_canon_sha256":"a85658ce5584dec41b368b20b85e82eef21d0a3c5b1f928bedf9f48c4b0bc526"},"schema_version":"1.0","source":{"id":"1512.04360","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04360","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04360v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04360","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"6237OTQVNPR2","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6237OTQVNPR2BAUA","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6237OTQV","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:2cd1940eeb859d7989559047dfdb73a0f8274db4beaeed9d2367671045dd0be2","target":"graph","created_at":"2026-05-18T01:24:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Suppose that $\\Sigma$ is a hyperbolic surface and $f:\\mathbb R_+\\to\\mathbb R_+$ a monotonic function. We study the closure in the projective tangent bundle $PT\\Sigma$ of the set of all geodesics $\\gamma$ satisfying $I(\\gamma,\\gamma)\\leq f(\\ell_\\Sigma(\\gamma))$. For instance we prove that if $f$ is unbounded and sublinear then this set has Hausdorff dimension strictly bounded between 1 and 3.","authors_text":"Anna Lenzhen, Juan Souto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-14T15:21:33Z","title":"Variations on a Theorem of Birman and Series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04360","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:35e9a527d199d8ac1eab60f8c31521c152647202a1bd55f536f399824c5f9832","target":"record","created_at":"2026-05-18T01:24:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ee5bebc4c377f40befc9491c4f0e17b7d72728b1272743cb44a598c2a7103b2b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-14T15:21:33Z","title_canon_sha256":"a85658ce5584dec41b368b20b85e82eef21d0a3c5b1f928bedf9f48c4b0bc526"},"schema_version":"1.0","source":{"id":"1512.04360","kind":"arxiv","version":1}},"canonical_sha256":"f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2","first_computed_at":"2026-05-18T01:24:22.382865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:22.382865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NBR5EoHvhPf+nabJn5h7LbwypLUZkI59B9ixrSBqPIeNDUzj27nHjB28LKchjsei64xFuerOdz2Vjx/cRAVJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:22.383476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04360","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e9a527d199d8ac1eab60f8c31521c152647202a1bd55f536f399824c5f9832","sha256:2cd1940eeb859d7989559047dfdb73a0f8274db4beaeed9d2367671045dd0be2"],"state_sha256":"97457e233163e72663fe7f888f840efea9cb75e7f277fee7f4c54f678bdb0a02"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHtemCFXgdX5/3tHjrFKM2YuhJdGxkrHAfqA8cTgUJmLAatFJo8CnUYvXdwMgC3ysMdSmx08VSwnSzpo2BKBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T16:06:06.397077Z","bundle_sha256":"2d0b524f09000d2726232b266de12d275472279bef475d57f69424d9989505ac"}}